Quantitative properties of oscillating-grid turbulence in a homogeneous fluid

Abstract

Oscillating-grid turbulence in a homogeneous uid is in equilibrium between the di usion of turbulent energy and the dissipation rate of the energy. Such a ÿeld has been investigated experimentally and analyzed by using the k-turbulence model. Vertical and horizontal components of uctuating velocity have been measured under the vertical oscillation of a square grid. Vertical proÿles of ÿve characteristic quantities, the turbulent energy k, the dissipation rate , the vertical energy ux F, the eddy viscosity t and a lengthscale lt, have been obtained from the measurements. In the model analysis, the governing equations and the boundary conditions have been non-dimensionalized by using the turbulent energy k0 and the dissipation rate 0 which are given virtually at the center of the grid oscillation as boundary conditions. Dimensionless analytical solutions of k; ; F; t and lt have been derived. The experimental data show some relationships existing between the analytical solutions. This shows the application of the k-model to the oscillating-grid turbulence to be valid. The analytical solutions include three model parameters. Their values have been determined from the experimental data. The values of k 0 and 0 have been evaluated by superposing the analytical solutions of k; and F on their experimental data, and have been related empirically to the experimental parameters. Using the empirical relations for k0 and 0 and the analytical solutions, we can estimate k; ; F; t and lt of the oscillating-grid turbulence.

Study of Gas Liquid Mass Transfer in a Grid Stirred Tank

“…These relationships have been verified by a number of studies using grid stirred tanks [24,25,[33][34][35][36][37][38] When studying the influence of oscillating grid turbulence on an interface, the distance z g = H between this interface and the mean position of the grid is of great importance. As one can see from HT, velocity fluctuations' intensity is an hyperbolic function of the distance to the grid, hence they tend to a zero asymptote far from the grid.…”

Modelling of sediment suspensions in oscillating grid turbulence

“…Our purpose is not to add another stone in these debates. The k -model was used before by Sonin (1983) and Matsunaga et al (1999) to describe purely di usive turbulence. When expressing the decay law in oscillating grid turbulence in the form of a power law (i.e.…”

The Role of Tep in Estuarine Hydrosedimentary Functioning: Impact on Settling Velocity of Aggregates

“…They are considered as of the same order of magnitude than the size of the largest flocs (Bouyer et al 2004, Mietta et al 2009. Average Kolmogorov microscale (η) corresponding to turbulent kinetic energy (TKE) generated by grid oscillations of 3 and 12 s period were 272 and 1021 µm, respectively (Matsunaga et al 1999, Jansen et al 2003, which was close to those measured in Cam estuary during dry season of 2009 for mid ebb and slack water; 256 and 950 µm, respectively.…”

“…For OGT, following Matsunaga et al (1999), dimensionless TKE (k ) and dimensionless TKE dissipation rate (ε ) can be expressed in an analytical form as: …”